Well, in English we would say "I don't like that shirt, can I have another one?" or "I need another piece of paper." Usually, it means there are two (or more) things alike, you need one like the one you have. We say "How many other shirts do you have?" (there are many shirts and this question is asking about all of them, not just one) or "I am going to a party with my friend Julie and the others." (there are many other friends that this is talking about). "Another" refers to one thing just like the one you have. "Other" usually refers to more than thing.

We use OTHER for plural nouns, and ANOTHER for singular.

"other" would be used to identify a different part of something for example; hand me my OTHER shoe. "another" would be used to identify a duplicate of the samething. for example; can i have ANOTHER pencil.